The review process for VCE Mathematics focused on:
 a comprehensive review of areas of study, topics, content, outcomes and key knowledge and key skills for all VCE Mathematics studies based on developments in the discipline, feedback during implementation, international benchmarking and the Australian
Curriculum senior secondary work.
 ensuring a range of studies which in their own right and in combination, provide accessibility, interest, applicability and challenge for a broad range of students, within a robust and flexible study structure.
 balance between conceptual and computational aspects of mathematics, which incorporates effective use of technology.
 the relationship between studies and assumed knowledge and skills for various pathways.
 a possible pathway from Foundations Mathematics Units 1 and 2 to Further Mathematics
Units 3 and 4.
 developing a distinct Specialist Mathematics Units 1 and 2 using the same flexible structure as for General Mathematics Units 1 and 2.
 re-development of Further Mathematics with a 60% core and 40% module structure.
 inclusion of statistics content in Mathematical Methods and Specialist Mathematics.

Refining School-assessed Coursework for all Units 3 and 4 studies based on two task types: Application task and Modelling or Problem solving task. The time allocation has been slightly reduced, and task specifications made more explicit. The test task type has been removed.

Work on ratios, proportions, percentages and rates, informal use of algebra and error, accuracy and tolerances has been strengthened.

Outcome 2 has been more aligned with the corresponding outcome in the other VCE mathematics studies, to emphasise problem solving in non-routine contexts as well as familiar contexts.

A pathway to Further Mathematics, depending on greater depth of treatment of material within the scope of the course, and a judicious selection of supplementary content related to the assumed knowledge and skills for Further Mathematics, in particular with respect to statistics.

The areas of study have been redeveloped as ‘Algebra and structure’, ‘Arithmetic and nu mber’, ‘Discrete mathematics’, ‘Geometry, measurement and trigonometry’, ‘Graphs of linear and nonlinear relations’ and ‘Statistics’ with revised topics throughout.

The statistical content has been re-developed as the topics Investigating and comparing data distributions and Investigating relationships between two numerical variables.

VCE MATHEMATICS
SUMMARY OF PROPOSED CHANGES

The former topic Integer and rational numbers systems has been re-developed as the topic Computation and practical arithmetic.

For Outcome 1, key knowledge and key skill statements have been written for each topic, rather than the group of topics within an area of study.

Further Mathematics Units 3 and 4 have been re-developed with a prescribed Core area of study Data analysis (40%) and Recursion and financial modelling (20%) and an
Applications area of study (40%) comprising two selected modules from four options
(previously three from six). The modules are: Matrices , Networks and decision mathematics , Geometry and measurement , and Graphs and relations .

The Matrices module includes a broader range of matrix types that can be used for modelling with simple recurrence relations.

The Geometry and measurement module incorporates spherical geometry and its application to the earth’s surface.
Unit 3 Outcomes and assessment
Outcomes Marks allocated* Assessment tasks
The Application task is a guided investigation of a given set of multivariate data. The task has three components of increasing complexity
- the construction, description and interpretation of data plots, including smoothed plots for time series data;
- the calculation and interpretation of summary statistics, including seasonal indices and their application for time series data;
- the modelling of linear associations or trends in time series data, including the use of data transformation when appropriate.
The application task is to be of 4–6 hours duration over a period of 1–2 weeks.
Modelling or problem solving task 1 is to be related to the topic Recursion and financial modelling. This task is to be of 2–3 hours duration over a period of 1 wee k.
Outcome 1
On completion of Unit 3 the student should be able to define and explain key terms and concepts as specified in the Core and use this knowledge to apply related mathematical techniques and models in a routine manner.
15
10
5
Application task
Modelling or problem solving task 1
Outcome 2
On completion of Unit 3 the student should be able to select and apply the mathematical concepts, models and techniques as specified in the Core in a range of contexts of increasing complexity.
30
20 Application task
10 Modelling or problem solving task 1
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VCE MATHEMATICS
SUMMARY OF PROPOSED CHANGES
Outcome 3
On completion of Unit 3 the student should be able to select and use, as required, the numeric, graphic, geometric, symbolic and statistical functionalities of their technology to develop mathematical ideas, produce results and carry out analysis in situations requiring problemsolving, modelling or investigative techniques or approaches.
Total marks
15
40
10
5
Application task
Modelling or problem solving task 1
Total marks 60
*School-assessed Coursework for Unit 3 contributes 20 per cent.
Unit 4 Outcomes and assessment
Outcomes
Outcome 1
On completion of Unit 4 the student should be able to define and explain key terms and concepts as specified for the modules studied and use this knowledge to apply related models and techniques to solve routine problems.
Marks allocated*
10
5
5
Assessment tasks
Modelling or problem solving task 2
Modelling or problem solving task 3
Outcome 2
On completion of Unit 4 the student should be able to select and apply the mathematical concepts, models and techniques as specified in the Core in a range of contexts of increasing complexity.
20
10
10
Modelling or problem solving task 2
Modelling or problem solving task 3
5 Modelling or problem solving task 2
Outcome 3
On completion of Unit 4 the student should be able to select and use, as required, the numeric, graphic, geometric, symbolic and statistical functionalities of their technology to develop mathematical ideas, produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches.
10
5 Modelling or problem solving task 3
Modelling or problem solving task 2 is related to the first selected module, Modelling or problem solving
task 3 is related to the second selected module.
The modelling or problem solving tasks are to be of
2–3 hours duration over a period of 1 week.
*School-assessed Coursework for Unit 4 contributes 14 per cent.
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VCE MATHEMATICS
SUMMARY OF PROPOSED CHANGES
 the Probability area of study has been extended to become the Probability and statistics area of study, with a new topic on sample proportions and confidence intervals included at
Units 3 and 4.
 content has been reduced across Units 1 –4, several topics have been removed completely and aspects of other topics removed throughout, in particular:
­ Markov chains/sequences and transition matrices
­ matrix representation and solution of simultaneous linear equations (this approach may be used but is not required)
­ the absolute value function and related graphs, transformations and equations
­ normal to graphs of functions
­ linear approximation of a function
­ compound angle formulas for sine, cosine and tangent
­ related rates of change
­ mode and median of a discrete probability distribution.
Unit 3 Outcomes and assessment
Outcomes
Outcome 1
On the completion of this unit the student should be able to define and explain key terms and concepts as specified in the content from the areas of study, and apply a range of related mathematical routines and procedures. It is expected that students will be able to use technology as applicable in the solution of problems, as well as apply routines and procedures by hand.
Outcome 2
On the completion of this unit the student should be able to apply mathematical processes, with an emphasis on general cases, in non-routine contexts, and analyse and discuss these applications of mathematics.
Outcome 3
On completion of this unit the student should be able to select and appropriately use numerical, graphical, symbolic and statistical functionalities of technology to develop mathematical ideas, produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches.
Marks allocated*
15
20
15
Assessment task
Application task
A function and calculus based mathematical investigation of a practical or theoretical context involving content from two or more areas of study, with three components of increasing complexity:
• introduction of the context through specific cases or examples;
• consideration of general features of the context; variation or further specification of assumption or conditions involved in the context to focus on a particular feature or aspect related to the context.
The application task is to be of 4–6 hours duration over a period of 1–2 weeks.
Total marks 50
*School-assessed Coursework for Unit 3 contributes 17 per cent.
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VCE MATHEMATICS
SUMMARY OF PROPOSED CHANGES
Unit 4 Outcomes and assessment
Outcomes
Outcome 1
On the completion of this unit the student should be able to define and explain key terms and concepts as specified in the content from the areas of study, and apply a range of related mathematical routines and procedures. It is expected that students will be able to use technology as applicable in the solution of problems, as well as apply routines and procedures by hand.
Marks allocated*
15
Outcome 2
On the completion of this unit the student should be able to apply mathematical processes, with an emphasis on general cases, in non-routine contexts, and analyse and discuss these applications of mathematics.
20
8
7
10
10
7
Outcome 3
On completion of this unit the student should be able to select and appropriately use numerical, graphical, symbolic and statistical functionalities of technology to develop mathematical ideas, produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches.
15
8
Assessment tasks
Modelling or problem solving task 1
Modelling or problem solving task 2
Modelling or problem solving task 1
Modelling or problem solving task 2
Modelling or problem solving task 1
Modelling or problem solving task 2
Total marks 50
One of the problem solving or modelling tasks is to be related to the Probability and statistics area of study.
The modelling or problem solving tasks are to be of
2–3 hours duration over a period of 1 week.
*School-assessed Coursework for Unit 4 contributes 17 per cent.

Specialist Mathematics Units 1 and 2 are two newly developed units, and utilise the same flexible structure and areas of study as General Mathematics Units 1 and 2, with a combination of prescribed topics and selected topics.

The prescribed topics for Specialist Mathematics Units 1 and 2 are: Number systems and recursion , Geometry in the plane and proof , Vectors in the plane , and Graphs of nonlinear relations.

Other topics for Specialist Mathematics Units 1 and 2 can be selected from additional new topics developed for advanced study of mathematics and/or those available for General
Mathematics Units 1 and 2.
©VCAA 2014 5

VCE MATHEMATICS
SUMMARY OF PROPOSED CHANGES
The following sample course for Specialist Mathematics Units 1 and 2 includes topics that cover a range of mathematical concepts and structures with opportunity for the study of proof and applications in a variety of contexts.
Unit 1
Unit 2
Arithmetic and number
Geometry, measurement and trigonometry
Number systems and recursion*
Graphs of linear and non-linear relations
Graphs of non-linear relations*
Geometry in the plane and proof*
Geometry, measurement and trigonometry
Vectors in the plane*
Algebra and structure
Arithmetic and number
Logic and algebra
Algebra and structure Transformations, trigonometry and matrices
Discrete mathematics Graph theory
Statistics Simulation, sampling and sampling distributions
Principles of counting Graphs of linear and non-linear relations
Kinematics
Three areas of study, five topics Four areas of study, five topics

Hyperbolas and ellipses has been removed as a separate minor topic and incorporated as required within regions of the complex plane and parametric paths in vector kinematics.

Several minor topics have been incorporated in a single topic on simple rational functions.

The absolute value function has been included.

A short topic on sample means and confidence intervals has been included (this extends on and complements related content in Mathematical Methods Units 3 and 4).
©VCAA 2014 6

VCE MATHEMATICS
SUMMARY OF PROPOSED CHANGES
Unit 3 Outcomes and assessment
Outcomes
Outcome 1
On the completion of this unit the student should be able to define and explain key terms and concepts as specified in the content from the areas of study, and apply a range of related mathematical routines and procedures. It is expected that students will be able to use technology as applicable in the solution of problems, as well as apply routines and procedures by hand.
Outcome 2
On the completion of this unit the student should be able to apply mathematical processes, with an emphasis on general cases, in non-routine contexts, and analyse and discuss these applications of mathematics.
Outcome 3
On completion of this unit the student should be able to select and appropriately use numerical, graphical, symbolic and statistical functionalities of technology to develop mathematical ideas, produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches.
Marks allocated*
15
20
15
Assessment task
Application task
A mathematical investigation of a practical or theoretical context involving content from two or more areas of study, with three components of increasing complexity:
– introduction of the context through specific cases or examples;
– consideration of general features of the context;
– variation or further specification of assumption or conditions involved in the context to focus on a particular feature or aspect related to the context.
The application task is to be of 4–6 hours duration over a period of 1–2 weeks.
Total marks 50
*School-assessed Coursework for Unit 3 contributes 17 per cent.
©VCAA 2014 7

VCE MATHEMATICS
SUMMARY OF PROPOSED CHANGES
Unit 4 Outcomes and assessment
Outcomes
Outcome 1
On the completion of this unit the student should be able to define and explain key terms and concepts as specified in the content from the areas of study, and apply a range of related mathematical routines and procedures. It is expected that students will be able to use technology as applicable in the solution of problems, as well as apply routines and procedures by hand.
Marks allocated*
15
Outcome 2
On the completion of this unit the student should be able to apply mathematical processes, with an emphasis on general cases, in non-routine contexts, and analyse and discuss these applications of mathematics.
Outcome 3
On completion of this unit the student should be able to select and appropriately use numerical, graphical, symbolic and statistical functionalities of technology to develop mathematical ideas, produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches.
20
15
8
10
7
10
7
8
Total marks 50
Assessment tasks
Modelling or problem solving task 1
Modelling or problem solving task 2
Modelling or problem solving task 1
Modelling or problem solving task 2
Modelling or problem solving task 1
Modelling or problem solving task 2
One of the problem solving or modelling tasks is to incorporate content related to probability and/or statistics.
The modelling or problem solving tasks are to be of
2–3 hours duration over a period of 1 week.
*School-assessed Coursework for Unit 4 contributes 17 per cent.
©VCAA 2014 8